Abstract :
The Type-II hidden symmetries are extra symmetries in addition to the inherited
symmetries of the differential equations when the number of independent and dependent
variables is reduced by a Lie point symmetry. In [B. Abraham-Shrauner, K.S. Govinder,
Provenance of Type II hidden symmetries from nonlinear partial differential equations,
J. Nonlinear Math. Phys. 13 (2006) 612–622] Abraham-Shrauner and Govinder have
analyzed the provenance of this kind of symmetries and they developed two methods
for determining the source of these hidden symmetries. The Lie point symmetries of a
model equation and the two-dimensional Burgers’ equation and their descendants were
used to identify the hidden symmetries. In this paper we analyze the connection between
one of their methods and the weak symmetries of the partial differential equation in
order to determine the source of these hidden symmetries. We have considered the same
models presented in [B. Abraham-Shrauner, K.S. Govinder, Provenance of Type II hidden
symmetries from nonlinear partial differential equations, J. Nonlinear Math. Phys. 13 (2006)
612–622], as well as the WDVV equations of associativity in two-dimensional topological
field theory which reduces, in the case of three fields, to a single third order equation
of Monge–Ampère type. We have also studied a second order linear partial differential
equation in which the number of independent variables cannot be reduced by using
Lie symmetries, however when is reduced by using nonclassical symmetries the reduced
partial differential equation gains Lie symmetries
